This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots. Special attention is paid to the design of extended Jacobian algorithms that approximate the Jacobian pseudoinverse algorithm. Two approaches to the approximation problem are developed: one relies on variational calculus, the other is differential geometric. Exampl...

This paper describes a comparative study of performance between the estimated image Jacobian that come from taking into account the geometry epipolar of a system of two cameras, and the well known analytic image Jacobian that is utilized for most applications in visual servoing. Image Based Visual Servoing architecture is used for controlling a 3 d.o.f. articular system using two cameras in eye...

The motion of a cutter tool is modeled as a surface undergoing a sweep operation along another geometric entity. A numerically controlled machining verification method is developed based on a formulation for delineating the volume generated by the motion of a cutting tool on the workpiece (stock). Varieties and subvarieties that are subsets of some Eucledian space defined by the zeros of a fini...

We consider the generalized Nash equilibrium problem (GNEP), where not only the players’ cost functions but also their strategy spaces depend on the rivals’ decision variables. Existence results for GNEPs are typically shown by using a fixed point argument for a certain set-valued function. Here we use a regularization of this set-valued function in order to obtain a single-valued function that...

This paper investigates the local uniqueness of designs of m-circles (lines and circles) in the plane up to inversion under a set of angles of intersection as constraints. This local behavior is studied through the Jacobian of the angle measurements in a form analogous to the rigidity matrix for a framework of points with distance constraints. After showing directly that the complete set of ang...

The computation of solution paths for continuation problems requires the solution of a sequence of nonlinear systems of equations. Each nonlinear system can be solved by computing the solution of a succession of linear systems of equations determined by Jacobian matrices associated with the nonlinear system of equations. Points on the solution path where the Jacobian matrix is singular are refe...